Statistical Methods

Introduction

A study was conducted measuring the different physical and cognitive effects of a new Dual Task exercise method in elderly participants. There were three treatment groups monitored, the Dual Task group, a standard exercise group referred to as Exercise Only, and a Control group. The goal of this study was to measure whether or not the Dual Task exercise plan had a significantly different cognitive and physical characteristics when compared to standard exercise. The study hopes to find whether the Dual Task group is more effective than standard exercise in this regard, in hopes it can help combat health decline and dementia in the elderly. In each of the three treatment groups, participants were measured at four separate time intervals, of which the first point was discarded due to incomplete data and the remaining points were divided into a baseline, six weeks out, and twelve weeks out. At each of these points, multiple variables of interest regarding cognition and physicality were measured.

Methods

Repeated Measures ANOVA

In order to investigate the effects of this new Dual Task method, we performed a 1-way repeated measures ANOVA test with a blocking factor of time to measure whether a difference in the variable of interest resulted in a group of interest at different time comparisons. The repeated measures ANOVA inherently accounts for variation in individual subjects, allowing us to The ANOVA was conducted at a confidence level of .05 and considered both the effects of group and time. The time comparisons were the baseline to six weeks, and six weeks to twelve weeks. The results of this ANOVA would decide whether there was a significant difference in the measured change in means of the variables of interest.

Null Hypothesis: There is no difference in the mean scores of the variables of interest between the three groups at all of timepoints.

Alternative Hypothesis: There is at least one difference in the mean scores of the variables of interest between the three groups at all of timepoints.

Paired T-Test

After the ANOVA results were obtained, pairwise t-tests were conducted at a .05 confidence level between all treatments and time comparisons of interest. The pairwise t-tests were used on all variables of interest, but will only be applicable in response variables that had significant ANOVA F tests. These pairwise t-tests were done to verify which group and time comparisons significantly differed from the others. This post-hoc analysis is integral to utilizing the ANOVA method.

Null Hypothesis: There is no difference in the scores of the variables of interest between the given two time points and the given group.

Alternative Hypothesis: There is a difference in the scores of the variables of interest between the given two time points and the given group.

Once these tests were run, the results were compiled into this flex-dashboard and analyzed to identify when treatments significantly differed. This was used to discern when the Dual Task exercise method resulted in a significant difference from the other two methods, which allowed us to make statistical conclusions regarding the effects of the treatment on the variables of interest. This analysis served to determine the efficacy of the Dual Task treatment as a whole.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Observing the graph, there appears to be little change in percent fat over time, save for one member of the exercise only group. This one individual appears to be an outlier, as there is no consistent pattern within any of the groups.

• ANOVA: According to the Anova test, the results are non-significant. With such a low F-Stat and a high P-value, the results of the pairwise t-test can be ignored. Percent-fat does not appear to vary significantly across groups over time.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Observing all graphs, there appears to be vary little change in systolic blood pressure in any group across time. One outlier exists with a systolic blood pressure of 0 in the baseline, but this is likely a data entry error.

• ANOVA: Observing the results of the Anova test, we fail to find any effect of treatment and time on systolic blood pressure. We cannot conclude that the means vary between group.

Graph

Anova Test

Table

Interpretation of Results

• Graph: There appears to be a slight downward trend in mean diastolic blood pressures within all groups, though this trend is driven by a few select individuals within groups. Observing the details of individual subjects, we see that within groups subjects diastolic blood pressure goes both up and down over time.

• ANOVA: The Anova test as a whole is non-significant, meaning that we did not find any evidence to suggest that the groups had different mean diastolic blood pressures at any point in time throughout the test.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, there appears to be little real change in resting heart rate over time throughout any of the groups. Individual subjects withing groups vary wildly, with resting heart rates increasing, decreasing, and remaining constant.

• ANOVA: Observing the Anova test results, we find that there is insufficient evidence to reject the null hypothesis. In other words, we can not conclude that groups had any differences in mean resting heart rate at any point in time.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Observing the chair stand lower body strength scores, they appear to be relatively constant across time within groups. The exercise only group had lower mean average chair strength at baseline, but the group mean soon converged to the other scores at week 6 and week 12.

• ANOVA: Observing the Anova test, our F-statitics is too low and p-value too high. This means that there is insufficient evidence to reject the null hypothesis, and we cannot conclude that chair stand lower body strength scores differ significantly between groups across time.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Observing the graphs it appears that timed up and go test scores (only walking) trend down over time from baseline to week 12. The effect is most pronounced in both the dual and exercise only groups. There is a “V” effect on the data, where the scores are lowest at week 6 across both dual and exeercise only groups, increasing slightly from week 6 to week 12.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Upon graphical observation, it appears that time up and go test scores (counting backward) trend downward over time throughout all groups, with the effects most pronounced in the dual and exercise only groups. Interestingly enough, the data appears to follow a “V” shape, with many subjects having their lowest score in week 6, and then having higher scores in week 12.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Observing the graphs, it appears that timed up and go test (holding water) scores trend downward over time in dual task and exercise only, while remaining somewhat constant in the control group. It is worth noting, in both dual and exercise only groups, the mean scores follow a “V” shape, with lowest mean scores at week 6, not week 12.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Observing the graph, it appears that timed up and go test scores (average of 3 conditions) trend down in the dual task group over time. In the exercise only group, from baseline to week 6 appears to trend down, while from week 6 to week 12 scores trend up. There is no discernible trend in the control group, with subjects showing constant, improved, and worsened scores.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Observing the graph, there appears to be a weak downward trend from baseline to week 12 in the Dual task group. There is a noticeable “V” shape here, implying that 4 square balance scores went up in the last period. This V-shape is present in Exercise only, but the trend is fat less noticeable. Finally, in the control group no trend is easily discernible.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, though group mean cognitive average scores appear to trend slightly up across all groups, individuals within those groups appear to have cognitive average scores that remain constant, increase, and decrease.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, it appears mean visuo-spatial scores increase over time in both dual and control, while remaining relatively constant in exercise only. However, subjects within these groups do not appear to follow this mean trend, meaning that these mean increases likely represent noise within the data.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, executive function appears to remain relatively constant across all groups over time. There appears to be no trend in subjects withing the groups.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: There does appear to be a slight upward trend in Naming/Language scores over time in both dual and control groups, but this trend is not reflected within the individual group’s subjects. The exercise only group appears to follow no real trend.

• ANOVA: With a low f-stat and high p-value (>.05), we can conclude that there is insufficient evidence to conclude that any groups scores significantly differ from the mean over time. With a p-value close to the cutoff, even the case where we raise the confidence interval to .10 remains inconclusive, since none of the pairwise t-tests are close to significant.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Memory scores appear to remain constant at all times throughout all groups. There appears to be two outlier subjects. One in the dual task group we showed a horrific drop in memory scores, and one in the control group which showed outstanding improvement.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Mean delayed recall appears to increase in all groups across time, though the trend in exercise only follows an inverted “V” shape, with highest scores in week 6 and not week 12. This “V” shape appears to be present in both normal and inverted forms in most subjects across all groups over time.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, mean abstraction scores appear to increase over time across all groups. Within individual groups, this trend does not appear to apply to subjects, with roughly equivalent levels of subjects showing increased, decreased, and constant abstraction scores over time.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: There appears to be a slight upward trend in level 2 smart fit voard scores over time across all groups. This trend does appear to be reflected by the individual subjects within specific treatments.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: In cognitive only scores (smart fit board level 2) there appears to be a very noticeable upward trend across all groups. The exercise only group is interesting because many subjects appear to follow an inverted “V” shaped trend. The subjects in this group peaked in week 6, making this the only group who’s week 12 score is not higher than their week 6 scores.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, there appears to be a noticeable trend in across all groups over time. All groups appear to show consistent improvement in mean dual task scores (SFB level 2) over time.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Observing the graphs, there appears to be no real trend in accuracy cognitive scores over time. The dual task group has one outlier that started very low, but increased to near mean levels.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Observing the graphs, there appears to be no real trend in accuracy dual task scores over time. The dual task group has one outlier that started very low, but increased to near mean levels.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: In the graph of cognititve only response time scores, it is clear that the mean scores decreases over time for all treatments. The decrease is most pronounced in the dual task and exercise only groups, and is consistently found across subject. It is worth noting, that for nearly every subject in every group, SFB level 2 response time cognitive only scores decreased.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored. While a trend appears to be present from the graph, the ANOVA shows no evidence of a within subjects trend.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, SFB level 2 response time dual task mean scores appear to decrease over time across all groups. This trend is reflective of the trends of individual subjects within these groups.

• ANOVA: With a low f-statistic and high p-value, the ANOVA test is insignificant. There is not enough evidence to conclude that response time is different between groups.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, there is little to no trend in the mean values of level 3 SFB physical scores across time. This is reflective of the subjects within these groups, as their scores vary between constant, improved, and worsened.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, there appears to be a slight upward trend in the means of the dual task group. However, this is not reflective of the subjects within the group, as their level 3 SFB cognitive only scores both increase and decrease over time dependent on subject. The exercise only and control groups appear to be relatively constant across time, with subjects in the groups improving, worsening, and remaining at constant values in roughly equal amounts.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, there appears to be a slight upward trend in dual task, with the mean level 3 SFB dual task scores increasing over time. The subjects within this group tend to either improve or remain constant. In the exercise only group, there appears to be no trend, however the control group also appears to trend upward similar to the dual task group.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, all groups appear to have a relatively constant mean SFB level 3 accuracy cognition score across time. Subjects appear to worsen, improve, and remain constant in equal amounts across all groups.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, dual and exercise only appear to have relatively constant SFB level 3 accuracy dual task scores over time, with subjects either increasing, decreasing, or maintaining constant scores. The control group appears to have increasing mean scores over time, though this is likely due to the significant amount of individuals who started at low scores and converged to the mean score level of the other groups.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, mean response time cognitive only SFB level 3 scores appear to decrease in dual task and exercise only groups, and this is reflected by the subjects within these groups. The mean scores for the control group appear to remain relatively constant, but a majority of the subjects within this group appear to experiences decreases in score.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, it appears that mean level 3 SFB response time-dual task scores decrease over time in the dual and exercise only task groups, while remaining constant in the control group. These mean trends are reflective of the subject trends within each group.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, mean visual motor reaction time scores appear to remain constant across time in all groups. This is reflective of the within subjects trends, as subjects either remain constant, increase, or decrease in score. From a graphical examination there does not appear to be any discernible trend in any group.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, mean visual salience reaction time scores appear to remain constant across time in all groups. This is reflective of the within subjects trends, as subjects either remain constant, increase, or decrease in score. From a graphical examination there does not appear to be any discernible trend in any group.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, mean adaptive motor control reaction time scores appear to remain constant across time in all groups. This is reflective of the within subjects trends, as subjects either remain constant, increase, or decrease in score. From a graphical examination there does not appear to be any discernible trend in any group.

• ANOVA: The ANOVA results in a high F-stat and a low p-value, which indicates that the ANOVA as a whole has found that there exists a significant difference between adaptive motor control reaction time between treatment groups. Observing the t-tests, we find that no single test is significant. This means we can’t state where the difference found by ANOVA is. This is likely due to differences in the power of the test. The t-tests do not have many subjects in each of them, so they have a lower power of the test than the ANOVA, which can utilize all of the subjects. A higher amount of subjects per group may allow us to make definitive conclusions in the future.

Graph

Anova Test

Table

Interpretation of Results

• Graph: Graphically, mean average executive function/average processing time scores appear to remain constant across time in all groups. This is reflective of the within subjects trends, as subjects either remain constant, increase, or decrease in score. There is 1 outlier in the exercise only group with a reaction time of 0, which either indicates a failed test or is an input error. From a graphical examination there does not appear to be any discernible trend in any group.

• ANOVA: The ANOVA results in a low F-stat and a high p-value, which indicates that the ANOVA as a whole is insignificant. There is not sufficient evidence to conclude that a difference in means occurs across time and group, and the results of the pairwise tests can be ignored.